Harrison was born in Washington, D.C., and graduated from Bard College, New York, in 1980 with a Bachelor of Arts in composition and performance.

Harrison has identified the Beatles, Jimi Hendrix, the Allman Brothers Band and Washington guitarist Danny Gatton as early influences.

[4] His work has included film scores, big-band projects,[4] and a collaboration with Indian sarod player Anupam Shobhakar titled Leave the Door Open (2013).

[7] The AllMusic website describes Harrison's style as an "electrifying blend of creative jazz, modern classical, and ethnic fusion",[4] while Down Beat magazine has rated him "a guitarist, composer and arranger of amazing skill and breadth".

[3] His collaborators have included Dave Liebman, Donny McCaslin, Gary Versace, David Binney, Dewey Redman, Norah Jones, Uri Caine and Christian Howes.